Topological Link Models of Multipartite Entanglement

Ning Bao1, Newton Cheng2, Sergio Hernández-Cuenca3, and Vincent Paul Su2

1Computational Science Initiative, Brookhaven National Lab, Upton, NY, 11973, USA
2Center for Theoretical Physics, Department of Physics, University of California, Berkeley, CA 94720, USA
3Department of Physics, University of California, Santa Barbara, CA 93106, USA

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We introduce a novel model of multipartite entanglement based on topological links, generalizing the graph/hypergraph entropy cone program. We demonstrate that there exist link representations of entropy vectors which provably cannot be represented by graphs or hypergraphs. Furthermore, we show that the contraction map proof method generalizes to the topological setting, though now requiring oracular solutions to well-known but difficult problems in knot theory.

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► References

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Cited by

[1] Sergio Hernández-Cuenca, Veronika E. Hubeny, and Massimiliano Rota, "The holographic entropy cone from marginal independence", Journal of High Energy Physics 2022 9, 190 (2022).

[2] Ning Bao and Joydeep Naskar, "Properties of the contraction map for holographic entanglement entropy inequalities", Journal of High Energy Physics 2024 6, 39 (2024).

[3] Dmitry Melnikov, "Entanglement classification from a topological perspective", Physical Review D 107 12, 126005 (2023).

[4] William Munizzi and Howard J. Schnitzer, "Entropy cones and entanglement evolution for Dicke states", Physical Review A 109 1, 012405 (2024).

[5] William Munizzi, "Bit by Bit: Gravity Through the Lens of Quantum Information", arXiv:2406.01695, (2024).

[6] Matteo Fadel and Sergio Hernández-Cuenca, "Symmetrized holographic entropy cone", Physical Review D 105 8, 086008 (2022).

[7] Howard J. Schnitzer, "The entropy cones of $W_N$ and $W_N^d$ states", arXiv:2204.04532, (2022).

[8] Temple He, Sergio Hernández-Cuenca, and Cynthia Keeler, "Beyond the Holographic Entropy Cone via Cycle Flows", arXiv:2312.10137, (2023).

The above citations are from Crossref's cited-by service (last updated successfully 2024-06-22 12:18:16) and SAO/NASA ADS (last updated successfully 2024-06-22 12:18:17). The list may be incomplete as not all publishers provide suitable and complete citation data.